On the Irreducibility of the Complex Specialization of the Representation of the Hecke Algebra of the Complex Reflection Group G_7

We consider a 2-dimensional representation of the hecke algebra h(g_7, u), where g_7 is the complex reflection group and u is the set of indeterminates u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3). after specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the representation of the hecke algebra h(g_7, u).